On the (Non)-Integrability of KdV Hierarchy with Self-consistent Sources

Non-holonomic deformations of integrable equations of the KdV hierarchy are studied by using the expansions over the so-called "squared solutions" (squared eigenfunctions). Such deformations are equivalent to perturbed models with external (self-consistent) sources. In this regard, the KdV6 equation is viewed as a special perturbation of KdV equation. Applying expansions over the symplectic basis of squared eigenfunctions, the integrability properties of the KdV hierarchy with generic self-consistent sources are analyzed. This allows one to formulate a set of conditions on the perturbation terms that preserve the integrability. The perturbation corrections to the scattering data and to the corresponding action-angle variables are studied. The analysis shows that although many nontrivial solutions of KdV equations with generic self-consistent sources can be obtained by the Inverse Scattering Transform (IST), there are solutions that, in principle, can not be obtained via IST. Examples are considered showing the complete integrability of KdV6 with perturbations that preserve the eigenvalues time-independent. In another type of examples the soliton solutions of the perturbed equations are presented where the perturbed eigenvalue depends explicitly on time. Such equations, however in general, are not completely integrable.Comment: 16 pages, no figures, LaTe

Chiral Symmetry Breaking and External Fields in the Kuperstein-Sonnenschein Model

A novel holographic model of chiral symmetry breaking has been proposed by Kuperstein and Sonnenschein by embedding non-supersymmetric probe D7 and anti-D7 branes in the Klebanov-Witten background. We study the dynamics of the probe flavours in this model in the presence of finite temperature and a constant electromagnetic field. In keeping with the weakly coupled field theory intuition, we find the magnetic field promotes spontaneous breaking of chiral symmetry whereas the electric field restores it. The former effect is universally known as the "magnetic catalysis" in chiral symmetry breaking. In the presence of an electric field such a condensation is inhibited and a current flows. Thus we are faced with a steady-state situation rather than a system in equilibrium. We conjecture a definition of thermodynamic free energy for this steady-state phase and using this proposal we study the detailed phase structure when both electric and magnetic fields are present in two representative configurations: mutually perpendicular and parallel.Comment: 50 pages, multiple figures, minor typo fixed, references adde

Imbalanced social-communicative and restricted repetitive behavior subtypes of autism spectrum disorder exhibit different neural circuitry

Social-communication (SC) and restricted repetitive behaviors (RRB) are autism diagnostic symptom domains. SC and RRB severity can markedly differ within and between individuals and may be underpinned by different neural circuitry and genetic mechanisms. Modeling SC-RRB balance could help identify how neural circuitry and genetic mechanisms map onto such phenotypic heterogeneity. Here, we developed a phenotypic stratification model that makes highly accurate (97-99%) out-of-sample SC = RRB, SC > RRB, and RRB > SC subtype predictions. Applying this model to resting state fMRI data from the EU-AIMS LEAP dataset (n = 509), we find that while the phenotypic subtypes share many commonalities in terms of intrinsic functional connectivity, they also show replicable differences within some networks compared to a typically-developing group (TD). Specifically, the somatomotor network is hypoconnected with perisylvian circuitry in SC > RRB and visual association circuitry in SC = RRB. The SC = RRB subtype show hyperconnectivity between medial motor and anterior salience circuitry. Genes that are highly expressed within these networks show a differential enrichment pattern with known autism-associated genes, indicating that such circuits are affected by differing autism-associated genomic mechanisms. These results suggest that SC-RRB imbalance subtypes share many commonalities, but also express subtle differences in functional neural circuitry and the genomic underpinnings behind such circuitry

Meson Spectra and Magnetic Fields in the Sakai-Sugimoto Model

We continue our study of the dynamics of the flavour sector of the Sakai-Sugimoto model in the presence of an external magnetic field, uncovering several features of the meson spectrum at high and low temperatures. We employ both analytical and numerical methods to study the coupled non-linear equations that result from the gravity dual.Comment: 44 pages, multiple figure

Saccade dysmetria indicates attenuated visual exploration in autism spectrum disorder

Background: Visual exploration in autism spectrum disorder (ASD) is characterized by attenuated social attention. The underlying oculomotor function during visual exploration is understudied, whereas oculomotor function during restricted viewing suggested saccade dysmetria in ASD by altered pontocerebellar motor modulation. Methods: Oculomotor function was recorded using remote eye tracking in 142 ASD participants and 142 matched neurotypical controls during free viewing of naturalistic videos with and without human content. The sample was heterogenous concerning age (6–30 years), cognitive ability (60–140 IQ), and male/female ratio (3:1). Oculomotor function was defined as saccade, fixation, and pupil-dilation features that were compared between groups in linear mixed models. Oculomotor function was investigated as ASD classifier and features were correlated with clinical measures. Results: We observed decreased saccade duration (∆M = −0.50, CI [−0.21, −0.78]) and amplitude (∆M = −0.42, CI [−0.12, −0.72]), which was independent of human video content. We observed null findings concerning fixation and pupil-dilation features (POWER =.81). Oculomotor function is a valid ASD classifier comparable to social attention concerning discriminative power. Within ASD, saccade features correlated with measures of restricted and repetitive behavior. Conclusions: We conclude saccade dysmetria as ASD oculomotor phenotype relevant to visual exploration. Decreased saccade amplitude and duration indicate spatially clustered fixations that attenuate visual exploration and emphasize endogenous over exogenous attention. We propose altered pontocerebellar motor modulation as underlying mechanism that contributes to atypical (oculo-)motor coordination and attention function in ASD

Optical Nanoantennas for Multiband Surface-Enhanced Infrared and Raman Spectroscopy

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Ensemble Analysis of Angiogenic Growth in Three-Dimensional Microfluidic Cell Cultures

We demonstrate ensemble three-dimensional cell cultures and quantitative analysis of angiogenic growth from uniform endothelial monolayers. Our approach combines two key elements: a micro-fluidic assay that enables parallelized angiogenic growth instances subject to common extracellular conditions, and an automated image acquisition and processing scheme enabling high-throughput, unbiased quantification of angiogenic growth. Because of the increased throughput of the assay in comparison to existing three-dimensional morphogenic assays, statistical properties of angiogenic growth can be reliably estimated. We used the assay to evaluate the combined effects of vascular endothelial growth factor (VEGF) and the signaling lipid sphingoshine-1-phosphate (S1P). Our results show the importance of S1P in amplifying the angiogenic response in the presence of VEGF gradients. Furthermore, the application of S1P with VEGF gradients resulted in angiogenic sprouts with higher aspect ratio than S1P with background levels of VEGF, despite reduced total migratory activity. This implies a synergistic effect between the growth factors in promoting angiogenic activity. Finally, the variance in the computed angiogenic metrics (as measured by ensemble standard deviation) was found to increase linearly with the ensemble mean. This finding is consistent with stochastic agent-based mathematical models of angiogenesis that represent angiogenic growth as a series of independent stochastic cell-level decisions